An investment group within Morgan Stanley offered to buy certain assets of a 2007-vintage Corsair Capital fund, in a deal that will allow investors to cash out early from a pool laden with boom-era bets, said people familiar with the matter.

The $1.1 billion Corsair III Financial Services Capital Partners LP was the first fund Corsair Capital’s team launched after spinning out from J.P. Morgan Chase & Co. in 2006. It now joins a...